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Unformatted text preview: Kata Bognar [email protected] Economics 142 Probabilistic Microeconomics UCLA Fall 2009 Homework Assignment 1. Suggested solutions  1. (Independence Axiom) Recall the Allais Paradox that we discussed in class. Con [6] sider the following four lotteries: A = $1 , 000 , 000 with probability 1 A = $5 , 000 , 000 with probability . 1 $1 , 000 , 000 with probability . 89 $0 with probability . 01 and B = $5 , 000 , 000 with probability . 1 $0 with probability . 9 B = $1 , 000 , 000 with probability . 11 $0 with probability . 89 . When people are asked to choose between A and A and between B and B they usually pick A and B , respectively. Show that such choices reveal preferences that do not satisfy the Independence Axiom. We write the lotteries A,A ,B and B in appropriate compound forms and point out that A A and the Independence Axiom together implies that B B. Therefore B B refutes the Independence Axiom. Define the following lotteries: • P is $1 , 000 , 000 for sure • Q is $0 for sure • R is $5 , 000 , 000 with probability 10 / 11 and $0 with probability 1 / 11. Then A = 0 . 11 P + 0 . 89 P and A = 0 . 11 R + 0 . 89 P while B = 0 . 11 R + 0 . 89 Q and B = 0 . 11 P + 0 . 89 Q. By the Independence Axiom if . 11 P + 0 . 89 P = A A = 0 . 11 R + 0 . 89 P then for every β ∈ [0 , 1] and lottery S , βP + (1 β ) S βR + (1 β ) S....
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 Fall '09
 Bognar
 Microeconomics, Game Theory, Utility, Professor Humbert

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